How Do You Solve This Complex Integral Involving Cosine and a Square Root?

[nemanja]

Hi,i would be gratefull if anyone could help me with this problem.

\frac{2}{\pi}\int \frac{cos(ux)}{\sqrt{x}} dx
x goes from zero to infinity.

thanks in advance.

 

[CompuChip]

Assuming you know a thing or two about Gaussian integrals, you could try substituting y^2 = x...

 

[nemanja]

yes I tried that and I got\frac{\sqrt{2}}{\sqrt{u\pi}}
but correct is \frac{1}{\sqrt{u}} .
any other way of solving?

 

[nicksauce]

Are you sure 1/√u is correct? Maple and wolfram alpha agree with your answer.

 

[nemanja]

Ok my mistake,thank you all.Maple rules